A combination is the number of ways a given number of objects can be selected from a group when the order does not matter (unlike a permutation, in which order does matter). If k objects are selected from a group of n members, the formula for the combination (which can be read as "n choose k") is

Combinations are important in probability as well as to the binomial theorem. All the possible combinations of an integer n make up the nth row of Pascal's triangle.

Example

How many different groups of three can be chosen from five people?

Since order is not important, we can use the formula for a combination.

Practice

Henry wants to choose 3 out of his 7 friends, how many ways can he do this?

Joe wants to choose 4 out of his 6 friends to go fishing with him. However, Jimmy and Andrew do not get along so they cannot be chosen together. How many ways can he do this?

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